Support Vector Classifiers in scikit-learn: Mathematical Detail, Part I

We present the mathematical detail pertaining to the theory of support vector classifiers, focusing our attention on hard-margin linear classifiers. We describe the rationale behind support vector classifiers, and provide extensive foundational detail. We construct the primal problem and, subsequently, derive the dual problem. We also show how the primal problem can be derived from the dual problem. The paper is the first in a series, and is intended to be educational in nature.